In Wachstein's Die Inschriften des Alten Judenfriedhofes in Wien › 1540 - 1670, page 117 et seq, he goes into detail about the confusion between Natan Feitel "The Elder" Esel, of Frankfurt and R' Nathan Veitel Teomim, A.B.D. of Worms and then Vienna who some sources say is the great-grandson of the former. Wachstein says it is pretty certain that the older Natan Feitel "The Elder" Esel, of Frankfurt is not the father of the younger Natan's grandfather Rabbi Moses Aharon Teomim-Fraenkel, because the older Natan Feitel of Frankfurt never went by the name Teomim. Wachstein says that Natan Feitel of Frankfurt could be one of the other great-grandfathers of Natan Feitel of Vienna, but is not certain which one. Wachstein sites a number of earlier sources that he says are clearly confusing the two, and are no doubt the source for some of the wrong information on this part of the tree.
In any case, I disconnected some seemingly wrong attachments and I think we should start from scratch and try to build the tree of the older Natan Feitel to see if it can be connected somehow to the younger one.